{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T11:55:17Z","timestamp":1782302117905,"version":"3.54.5"},"reference-count":48,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,12,14]],"date-time":"2025-12-14T00:00:00Z","timestamp":1765670400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Graduate Studies and Scientific Research, Jazan University, Saudi Arabia","award":["JU-20250228-DGSSR-RP-2025"],"award-info":[{"award-number":["JU-20250228-DGSSR-RP-2025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>This study introduces an innovative Honey Badger Optimization (HBO) designed to address the Optimal Power Flow (OPF) challenge in electrical power systems. HBO is a unique population-based searching method inspired by the resourceful foraging behavior of honey badgers when hunting for food. In this algorithm, the dynamic search process of honey badgers, characterized by digging and honey-seeking tactics, is divided into two distinct stages, exploration and exploitation. The OPF problem is formulated with objectives including fuel cost minimization and voltage deviation reduction, alongside operational constraints such as generator limits, transformer settings, and line power flows. HBO is applied to the IEEE 30-bus test system, outperforming existing methods such as Particle Swarm Optimization (PSO) and Gray Wolf Optimization (GWO) in both fuel cost reduction and voltage profile enhancement. Results indicate significant improvements in system performance, achieving 38.5% and 22.78% better voltage deviations compared to GWO and PSO, respectively. This demonstrates HBO\u2019s efficacy as a robust optimization tool for modern power systems. In addition to the single-objective studies, a multi-objective OPF formulation was investigated to produce the complete Pareto front between fuel cost and voltage deviation objectives. The proposed HBO successfully generated a well-distributed set of trade-off solutions, revealing a clear conflict between economic efficiency and voltage quality. The Pareto analysis demonstrated HBO\u2019s strong capability to balance these competing objectives, identify knee-point operating conditions, and provide flexible decision-making options for system operators.<\/jats:p>","DOI":"10.3390\/biomimetics10120836","type":"journal-article","created":{"date-parts":[[2025,12,16]],"date-time":"2025-12-16T08:46:52Z","timestamp":1765874812000},"page":"836","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Multidimensional Optimal Power Flow with Voltage Profile Enhancement in Electrical Systems via Honey Badger Algorithm"],"prefix":"10.3390","volume":"10","author":[{"given":"Sultan Hassan","family":"Hakmi","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronics Engineering, Faculty of Engineering and Computer Science, Jazan University, Jizan 45142, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hashim","family":"Alnami","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, Faculty of Engineering and Computer Science, Jazan University, Jizan 45142, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1441-2770","authenticated-orcid":false,"given":"Badr M. Al","family":"Faiya","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, Faculty of Engineering and Computer Science, Jazan University, Jizan 45142, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9394-5251","authenticated-orcid":false,"given":"Ghareeb","family":"Moustafa","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, Faculty of Engineering and Computer Science, Jazan University, Jizan 45142, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"158353","DOI":"10.1109\/ACCESS.2021.3127940","article-title":"Stochastic Modeling for Wind Energy and Multi-Objective Optimal Power Flow by Novel Meta-Heuristic Method","volume":"9","author":"Khamees","year":"2021","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Sarhan, S., Shaheen, A.M., El-Sehiemy, R.A., and Gafar, M. (2022). Enhanced Teaching Learning-Based Algorithm for Fuel Costs and Losses Minimization in AC-DC Systems. Mathematics, 10.","DOI":"10.3390\/math10132337"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Alqahtani, M.H., Almutairi, S.Z., Shaheen, A.M., and Ginidi, A.R. (2024). Enhanced Kepler Optimization Method for Nonlinear Multi-Dimensional Optimal Power Flow. Axioms, 13.","DOI":"10.3390\/axioms13070419"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.aej.2024.02.069","article-title":"Optimal operation and control of hybrid power systems with stochastic renewables and FACTS devices: An intelligent multi-objective optimization approach","volume":"93","author":"Premkumar","year":"2024","journal-title":"Alex. Eng. J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1109\/59.744492","article-title":"A review of selected optimal power flow literature to 1993. I. Nonlinear and quadratic programming approaches","volume":"14","author":"Momoh","year":"1999","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1016\/j.ijepes.2018.12.008","article-title":"Linear\/quadratic programming-based optimal power flow using linear power flow and absolute loss approximations","volume":"107","author":"Fortenbacher","year":"2019","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_7","first-page":"101265","article-title":"Economic and environmental optimization-dispatch in large-scale power systems using weighted mean of vectors algorithm","volume":"48","author":"Shaheen","year":"2025","journal-title":"Sustain. Comput. Inform. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"135929","DOI":"10.1109\/ACCESS.2024.3461805","article-title":"Enhanced Aquila Optimizer for Economic Environmental Dispatch with Cubic Fuel Cost and Emission Models","volume":"12","author":"Aljumah","year":"2024","journal-title":"IEEE Access"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2535","DOI":"10.1016\/j.egyr.2025.09.016","article-title":"A novel Kangaroo Escape Algorithm for efficient combined heat and power economic dispatch: Feasibility analysis and validations","volume":"14","author":"Aljumah","year":"2025","journal-title":"Energy Rep."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.aej.2024.07.007","article-title":"Developing artificial hummingbird algorithm with linear controlling strategy and diversified territorial foraging tactics for combined heat and power dispatch","volume":"105","author":"Shaheen","year":"2024","journal-title":"Alex. Eng. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1285","DOI":"10.1080\/15325008.2012.689417","article-title":"Optimal power flow using adapted genetic algorithm with adjusting population size","volume":"40","author":"Attia","year":"2012","journal-title":"Electr. Power Compon. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1080\/15325008.2021.1937389","article-title":"A PSO Optimal Power Flow (OPF) Method for Autonomous Power Systems Interconnected with HVDC Technology","volume":"49","author":"Syllignakis","year":"2021","journal-title":"Electr. Power Compon. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"107421","DOI":"10.1016\/j.asoc.2021.107421","article-title":"Fitness\u2013Distance Balance based adaptive guided differential evolution algorithm for security-constrained optimal power flow problem incorporating renewable energy sources","volume":"108","author":"Guvenc","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1270","DOI":"10.1109\/JSYST.2021.3076515","article-title":"Optimal Economic\u2013Environmental Operation for AC-MTDC Grids by Improved Crow Search Algorithm","volume":"16","author":"Shaheen","year":"2021","journal-title":"IEEE Syst. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"106321","DOI":"10.1016\/j.asoc.2020.106321","article-title":"Application of modified pigeon-inspired optimization algorithm and constraint-objective sorting rule on multi-objective optimal power flow problem","volume":"92","author":"Chen","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"584","DOI":"10.1080\/15325008.2021.1971331","article-title":"Optimal Power Flow via Teaching-Learning-Studying-Based Optimization Algorithm","volume":"49","author":"Akbari","year":"2021","journal-title":"Electr. Power Compon. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"El-Sehiemy, R., Elsayed, A., Shaheen, A., Elattar, E., and Ginidi, A. (2021). Scheduling of Generation Stations, OLTC Substation Transformers and VAR Sources for Sustainable Power System Operation Using SNS Optimizer. Sustainability, 13.","DOI":"10.3390\/su132111947"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"9448199","DOI":"10.1155\/2022\/9448199","article-title":"Optimal Power Flow Incorporating Thyristor-Controlled Series Capacitors Using the Gorilla Troops Algorithm","volume":"2022","author":"Ginidi","year":"2022","journal-title":"Int. Trans. Electr. Energy Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/j.epsr.2016.09.025","article-title":"Optimal power flow using moth swarm algorithm","volume":"142","author":"Mohamed","year":"2017","journal-title":"Electr. Power Syst. Res."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Kumar, P., Kalam, A., and Paul, K. (2024). Optimal Power Flow Analysis Using Pelican Optimization Algorithm. Lecture Notes in Electrical Engineering, Springer Nature.","DOI":"10.1007\/978-981-99-8289-9_7"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Al-Kaabi, M., Dumbrava, V., and Eremia, M. (2023, January 29\u201330). Application of Harris Hawks Optimization in Single Objective Optimal Power Flow. Proceedings of the 15th International Conference on Electronics, Computers and Artificial Intelligence, ECAI 2023, Bucharest, Romania.","DOI":"10.1109\/ECAI58194.2023.10194019"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Choudhary, J.K., Rohan, R., Tanti, D.K., Kumari, N., and Kumar, P. (2023, January 13\u201315). Application of Zebra Optimisation Algorithm for Solving Optimal Power Flow Issues. Proceedings of the OCIT 2023\u201421st International Conference on Information Technology, Raipur, India.","DOI":"10.1109\/OCIT59427.2023.10431341"},{"key":"ref_23","first-page":"36","article-title":"A Review of State-of-the-Art Techniques for Power Flow Analysis","volume":"4","author":"Sabo","year":"2023","journal-title":"J. Sci. Technol. Eng. Res."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Gupta, S., Kumar, N., Srivastava, L., Malik, H., Marug\u00e1n, A.P., and M\u00e1rquez, F.P.G. (2021). A hybrid jaya\u2013powell\u2019s pattern search algorithm for multi-objective optimal power flow incorporating distributed generation. Energies, 14.","DOI":"10.3390\/en14102831"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Khan, A., Hizam, H., Wahab, N.I.B.A., and Othman, M.L. (2020). Optimal power flow using hybrid firefly and particle swarm optimization algorithm. PLoS ONE, 15.","DOI":"10.1371\/journal.pone.0235668"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"184468","DOI":"10.1109\/ACCESS.2019.2958279","article-title":"Hybrid harris hawk optimization based on differential evolution (HHODE) algorithm for optimal power flow problem","volume":"7","author":"Birogul","year":"2019","journal-title":"IEEE Access"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1080\/0952813X.2022.2040598","article-title":"Merging slime mould with whale optimization algorithm for optimal allocation of hybrid power flow controller in power system","volume":"35","author":"Bhandakkar","year":"2023","journal-title":"J. Exp. Theor. Artif. Intell."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.matcom.2021.08.013","article-title":"Honey Badger Algorithm: New metaheuristic algorithm for solving optimization problems","volume":"192","author":"Hashim","year":"2022","journal-title":"Math. Comput. Simul."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3991870","DOI":"10.1155\/2022\/3991870","article-title":"Enhanced Feature Selection Based on Integration Containment Neighborhoods Rough Set Approximations and Binary Honey Badger Optimization","volume":"2022","author":"Hosny","year":"2022","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"8507","DOI":"10.1016\/j.aej.2022.02.009","article-title":"Comparison among different recent metaheuristic algorithms for parameters estimation of solid oxide fuel cell: Steady-state and dynamic models","volume":"61","author":"Yakout","year":"2022","journal-title":"Alex. Eng. J."},{"key":"ref_31","first-page":"102005","article-title":"Model identification of proton-exchange membrane fuel cells based on a hybrid convolutional neural network and extreme learning machine optimized by improved honey badger algorithm","volume":"52","author":"Han","year":"2022","journal-title":"Sustain. Energy Technol. Assess."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Rawa, M., Abusorrah, A., Al-Turki, Y., Calasan, M., Micev, M., Ali, Z.M., Mekhilef, S., Bassi, H., Sindi, H., and Aleem, S.H.E.A. (2022). Estimation of Parameters of Different Equivalent Circuit Models of Solar Cells and Various Photovoltaic Modules Using Hybrid Variants of Honey Badger Algorithm and Artificial Gorilla Troops Optimizer. Mathematics, 10.","DOI":"10.3390\/math10071057"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/j.egyr.2022.05.168","article-title":"Photovoltaic parameter estimation using honey badger algorithm and African vulture optimization algorithm","volume":"8","author":"Diab","year":"2022","journal-title":"Energy Rep."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3199","DOI":"10.32604\/iasc.2023.029804","article-title":"Honey Badger Algorithm Based Clustering with Routing Protocol for Wireless Sensor Networks","volume":"35","author":"Arutchelvan","year":"2023","journal-title":"Intell. Autom. Soft Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"108617","DOI":"10.1109\/ACCESS.2023.3320931","article-title":"The Coverage Improvement of the Wireless Sensor Network Based on the Parameters Optimized Honey Badger Algorithm","volume":"11","author":"Luo","year":"2023","journal-title":"IEEE Access"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/j.egyr.2023.10.002","article-title":"A novel honey badger algorithm based load frequency controller design of a two-area system with renewable energy sources","volume":"9","author":"Ozumcan","year":"2023","journal-title":"Energy Rep."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s12530-023-09495-z","article-title":"Honey Badger algorithm using lens opposition based learning and local search algorithm","volume":"15","author":"Majumdar","year":"2024","journal-title":"Evol. Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3943","DOI":"10.1007\/s11227-023-05560-1","article-title":"A novel honey badger algorithm with multilayer perceptron for predicting COVID-19 time series data","volume":"80","author":"Qasem","year":"2024","journal-title":"J. Supercomput."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2432","DOI":"10.1002\/oca.3164","article-title":"Optimal allocation of solar photovoltaic distributed generation for performance enhancement of electrical distribution networks considering optimal volt-var regulation under uncertainty and high load variation","volume":"45","author":"Hareche","year":"2024","journal-title":"Optim. Control Appl. Methods"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/j.comcom.2023.08.011","article-title":"An optimized multi-hop routing protocol for wireless sensor network using improved honey badger optimization algorithm for efficient and secure QoS","volume":"214","author":"Altuwairiqi","year":"2024","journal-title":"Comput. Commun."},{"key":"ref_41","first-page":"47","article-title":"An Improved Honey Badger Algorithm for Solving Congestion Management of Power System Considering Effective of Renewable Energy Resources","volume":"18","author":"Duong","year":"2025","journal-title":"Int. J. Intell. Eng. Syst."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Ting, H., Yong, C., and Peng, C. (2025). Improved Honey Badger Algorithm Based on Elite Tangent Search and Differential Mutation with Applications in Fault Diagnosis. Processes, 13.","DOI":"10.3390\/pr13010256"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"120843","DOI":"10.1016\/j.enconman.2025.120843","article-title":"Optimal photovoltaic system placement on the distribution grid by applying modified honey badger algorithm in the probabilistic framework","volume":"349","author":"Barutcu","year":"2026","journal-title":"Energy Convers. Manag."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"El-Sehiemy, R., Shaheen, A., Ginidi, A., and Elhosseini, M. (2022). A Honey Badger Optimization for Minimizing the Pollutant Environmental Emissions-Based Economic Dispatch Model Integrating Combined Heat and Power Units. Energies, 15.","DOI":"10.3390\/en15207603"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"7923","DOI":"10.1007\/s00521-024-09485-5","article-title":"Robust generation expansion planning in power grids under renewable energy penetration via honey badger algorithm","volume":"36","author":"Shaheen","year":"2024","journal-title":"Neural Comput. Appl."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"16765","DOI":"10.1038\/s41598-023-43622-9","article-title":"Reliability constrained dynamic generation expansion planning using honey badger algorithm","volume":"13","author":"Shaheen","year":"2023","journal-title":"Sci. Rep."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"110426","DOI":"10.1016\/j.asoc.2023.110426","article-title":"TLBO merged with studying effect for Economic Environmental Energy Management in High Voltage AC Networks Hybridized with Multi-Terminal DC Lines","volume":"143","author":"Sarhan","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1080\/1448837X.2017.1325134","article-title":"Optimal reactive power dispatch using backtracking search algorithm","volume":"13","author":"Shaheen","year":"2016","journal-title":"Aust. J. Electr. Electron. Eng."}],"container-title":["Biomimetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-7673\/10\/12\/836\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T10:09:37Z","timestamp":1765966177000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-7673\/10\/12\/836"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,14]]},"references-count":48,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["biomimetics10120836"],"URL":"https:\/\/doi.org\/10.3390\/biomimetics10120836","relation":{},"ISSN":["2313-7673"],"issn-type":[{"value":"2313-7673","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,14]]}}}